Problem: Simplify the following expression: $p = \dfrac{-44z^3 + 11z^2}{-110z^3 + 11z^2}$ You can assume $z \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-44z^3 + 11z^2 = - (2\cdot2\cdot11 \cdot z \cdot z \cdot z) + (11 \cdot z \cdot z)$ The denominator can be factored: $-110z^3 + 11z^2 = - (2\cdot5\cdot11 \cdot z \cdot z \cdot z) + (11 \cdot z \cdot z)$ The greatest common factor of all the terms is $11z^2$ Factoring out $11z^2$ gives us: $p = \dfrac{(11z^2)(-4z + 1)}{(11z^2)(-10z + 1)}$ Dividing both the numerator and denominator by $11z^2$ gives: $p = \dfrac{-4z + 1}{-10z + 1}$